Imagine an economy with many firms and workers. The economy satisfies the usual
ID: 1120844 • Letter: I
Question
Imagine an economy with many firms and workers. The economy satisfies the usual assumptions of the perfectly competitive model with the exception that firms and workers have different types. The firms are of two types and can be distinguished by their zero-profit isoprofit curves. Firms of the first type have a curves whose equation is w1 = 6/(r 5) + 20, where w1 is the value of wage paid by those firms and r is the riskiness of jobs they offer. Similarly, firms of the second type have a curve whose equation is w2 = 5/(r 1) + 10. Also, the minimum risk achievable for the firms of type 1 is r = 5.3 and for the firms of type 2 it is r = 1.5.
In addition to firms, there are two types of workers in this economy. They differ by their utility functions: type 1 has utility function u1(w, r) = w r^ (7/4) and type 2 has utility function u2(w, r) = w r^6/5.
Lastly, the slope of the isoprofit curve for type 1 firms is given by 5/(r 1)^2 and for type 2 firms it is given by 6/(r 5)^2 . For workers, MRS1 = (7/4)*r^ 3/4 and MRS2 = (6/5)*r^1/5 . Using this information please answer the following questions.
(a) Accurately sketch the zero-profit isoprofit curves for both types of firms on the same set of coordinates. Please, make sure that the level of risk is plotted along the horizontal axis. Comment what the sketch tells us about the riskiness of jobs at the two types of firms.
(b) Now, separately, sketch the the indifference curves for the level of utility ¯u = 3 for both types of workers. Which type of workers is more risk-averse and which is less risk-averse?
(c) Now argue graphically, with a new sketch, and verbally which type of workers will be matched with with type of firms in an equilibrium.
(d) Mathematically support your argument in part (c) by finding equilibrium wages and risk levels of the jobs chosen by workers of type 1 and 2.
Note that about half of the points for this problem is allocated to part (d).
Explanation / Answer
a. Finally a utility of 200S A required by each worker
for worker 1 E EPHI provided then U =100+]0 =170 therfore he would prefer a wage of 2005 to sat., himself
for worker 2 if EPHI provided then U =100 +110 =210 > 20011f no ephi) therfore he would prefer a Health insurance to satisfy himself..
for worker 3 if EPHI provided then U =100 +160 = 260 > 200( if no eph) therfore he would prefer a Health insurance. satisfy himself..
+Majority satisfaction..workers will HAVE EPHI